We will assume that the initial distribution of those PBHs is sufficiently uniform and dilute that PBH collisions are negligible. The first problem to address is then the evolution of a black hole of initial mass \(M\)  in a radiation dominated universe. This was first studied by Novikov and Zeldovitch[1]} followed by work of Carter and Hawking[2]}. The conclusion of these studies is that if the initial radiation dominated energy density is much less than the Planck scale, then black holes do not typically grow very much during a radiation dominated era. When the radiation temperature falls below the Hawking temperature, they decay at roughly the rate of decay in flat space. The fixed line of solutions found in[1]}, where the black hole grows to fill the horizon, is unstable.
